Methods and systems for determining manufacturing and operating parameters for a deviated downhole well component

ABSTRACT

Systems and methods for determining manufacturing or operating parameters for a deviated downhole well component, including a method that includes representing a tubular string as nodes separated by segments, determining transfer matrices for determining an i th  node&#39;s state vector from an i th −1 node&#39;s state vector, and defining initial state vector values for the reference node. The nodes are numerable from 1 to N with an initial, mechanically constrained reference node representable with i=0, and each is associated with a state vector describing a corresponding node position and one or more forces present at said node. The method further includes applying the transfer matrices to obtain each of the state vectors&#39; values, deriving from at least one of the state vectors a parameter value for said component, and specifying a component having said parameter value. The parameter value can include a centralizer or stabilizer composition, manufacturing dimensions, or position.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to Provisional U.S. Application Ser.No. 61/837,986, titled “Methods and Systems for Modeling a DeviatedDownhole Well Component” and filed Jun. 21, 2013 by Robello Samuel andZhenying Wang, which is incorporated herein by reference.

BACKGROUND

As world demand for petrochemical products has continued to increase,oil and gas companies have had to expand their exploration andproduction efforts into developing increasingly deep wells. As a result,the structures constructed to form a well must be capable of operatingunder larger loads and stresses than ever before. Because failures canhave costly consequences, it is important to design all well structureswith appropriate safety margins.

One example of such a structure is the well casing. A well casing is atubular structure generally made of a steel pipe surrounded by aconcrete layer that secures the steel pipe to the surrounding formation,thus defining the outside wall of the well. The concrete providessupport to the steel pipe, as well as additional isolation layer betweenthe formation and fluids flowing within the casing. In order todetermine the correct materials and dimensions for the various casingcomponents, engineers frequently perform computer simulations to modelvarious casing configurations under simulated downhole conditions. Thesimulations provide the engineer with information regarding the variousloads and stresses to which the casing might be subjected, and enablepotential designs to be evaluated.

But casing designs are only as good as the underlying simulation model.While simulations of single section casings in vertical wells aregenerally well understood and produce accurate results, tapered casings,deviated casings and casings with fluid flow restrictions representindeterminate complex mechanical systems that can be very difficult orimpractical to model using existing techniques. While methods do existwherein these more complex systems are modeled as simpler single-sectionvertical wells with the results being adjusted to include additionalsafety margins, such methods can incur a significant risk, given thelack of quantifiable data to support the selected margins.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the various disclosed embodiments can beobtained when the following detailed description is considered inconjunction with the attached drawings, in which:

FIG. 1 shows an illustrative downhole well with a well casing modeledusing the disclosed systems and methods.

FIG. 2 shows the various parameters describing the forces operating onan illustrative well casing string segment.

FIG. 3 shows an illustrative computer system suitable for performing thedisclosed methods.

FIG. 4 shows an illustrative example of the disclosed methods.

It should be understood that the drawings and corresponding detaileddescription do not limit the disclosure, but on the contrary, theyprovide the foundation for understanding all modifications, equivalents,and alternatives falling within the scope of the appended claims.

DETAILED DESCRIPTION

The paragraphs that follow describe illustrative systems and methods fordetermining manufacturing or operating parameters for a deviateddownhole well component. Examples are provided within the context of atapered and deviated well casing that is mechanically constrained atopposite ends. The mechanics of such a casing are explained andillustrated, and matrices are presented that mathematically describe theknown and unknown forces acting at various points along the casing.Finally, methods and systems are described that combine the variousmatrices to compute the forces present along the casing.

The disclosed systems and methods are best understood when described inan illustrative usage context. Accordingly, FIG. 1 shows an illustrativedrilling environment. A drilling platform 2 supports a derrick 4 havinga traveling block 6 for raising and lowering a drillstring 8 intoborehole 30. A top drive 10 supports and rotates the drillstring 8 as itis lowered through the wellhead 12. A pump 20 circulates drilling fluidthrough a feed pipe 22 to top drive 10, downhole through the interior ofdrill string 8, through orifices in a downhole tool (not shown), back tothe surface via the annulus around drillstring 8, and into a retentionpit 24. The drilling fluid aids in maintaining the borehole integrity.

Because boreholes are routinely drilled to ten thousand feet or more indepth and can be steered horizontally for perhaps twice that distance, awell casing string is inserted into the borehole and is cemented to theborehole wall to provide support to the borehole and isolation betweenthe formation and the fluids flowing within the well casing string. Inthe example of FIG. 1, the upper end of well casing string 14 isattached to and mechanically constrained by casing hanger 15, located atthe end of casing header 11. As well casing string 14 extends downholeit may be tapered to provide additional support between the casingstring and the borehole wall and to reduce the overall weight of thestring. Well casing string 14 of FIG. 1, for example, includes taperedreductions 13 and 15. Well casing string 14 also curves to conform tothe shape of the deviated well shown. A shoe 16 is located at the end ofwell casing string 14, wherein shoe 16 and stabilizers 18 fix andmechanically constrain the lower end of well casing string 14 withinborehole 30.

As can be seen in the illustrative example of FIG. 1, prior to beingcemented to the borehole wall, well casing string 14 is supported andmechanically constrained by just two points at either end of the wellcasing string. The deviation of the well casing string, as well as thereductions in the cross-sectional are of the well casing string at thereductions, produce complex three-dimensional forces that act upon thewell. The resulting service load distribution on the well casing stringcauses the string to become a statically complicated indeterminatemechanical system. Piston forces acting on plugs within the casing(e.g., cementing plugs) also produce forces similar to those at thereduction, further complicating the system.

In at least some illustrative embodiments, the forces acting on theabove-described well casing string are modeled by dividing the systeminto a series of N subsystems that each only interact with adjacentsubsystems, and then determining the forces acting on each subsystem insequence. FIG. 2 shows an illustrative well casing string subsystemidentified as segment 202 that is defined by two nodes 204 and 206. Eachnode is described by a state vector that includes information regardingthe location of the node relative to a reference node, and also includesinformation describing the forces present at the node. Each illustrativestate vector is defined as,

V _(i) =[u _(i) v _(i)α_(i) F _(xi) F _(hi) M _(i)−1]_(i) ^(T)  (1)

where,

u_(i) is the true vertical depth (TVD) of node i relative to thereference node;

v_(i) is the horizontal distance of node i from the reference node;

α_(i) is the inclination angle of the casing segment at node i;

F_(xi) is the vertical force present at node i;

F_(hi) is the horizontal force present at node i; and

M_(i) is the bending moment present at node i.

The reference node of the illustrative example is located at the casinghanger and is designated as node 0, and the node at the opposite end ofthe well casing string and furthest away from node 0 is designated asnode N.

After dividing the illustrative well casing string into segments, theunknown forces acting on each segment's downhole node are determined bystarting at the reference node at one end of the first segment (whereall elements of the state vector are known) and determining the statevector for the next node at the opposite end of the segment. The statevector for the downhole node of the first segment is determined bycomputing a cross product of a transfer matrix and the reference node'sstate vector. This transfer matrix is defined based upon the knownelements of the downhole node's state vector, the previous node's statevector and/or the reference node's state vector. For the first segmentthe previous node is also the reference node (i.e., i−1=0). In at leastsome illustrative embodiments, the transfer matrix T_(i) for a wellcasing string segment defined between nodes i and i−1 is described usingknown state vector elements as,

$\begin{matrix}\begin{bmatrix}1 & 0 & {- l_{i}^{h}} & \left( {\frac{\left( l^{h_{i}} \right)^{B}}{6 \times ({EI})_{i}} + \frac{l_{i}^{x}}{({EA})_{i}}} \right) & 0 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{h}}} \\0 & 1 & l_{i}^{x} & 0 & \left( {{- \frac{\left( l_{i}^{x} \right)^{B}}{6 \times ({EI})_{i}}} + \frac{l_{i}^{h}}{({EA})_{i}}} \right) & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{x}}} \\0 & 0 & 1 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & \frac{\sqrt{\left( l_{i}^{x} \right)^{2} + \left( l_{i}^{h} \right)^{2}}}{({EI})_{i}} & {\Delta \; \alpha_{i}^{0}} \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & l_{i}^{h} & {- l_{i}^{x}} & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i} & (2)\end{matrix}$

where,

-   -   l_(i) ^(h) is the horizontal distance defined as        (v_(i)−v_(i−1));    -   l_(i) ^(x) is the vertical distance defined as (u_(i)−u_(i−1));    -   Δα_(i−1) ⁰ is the change in inclination angle at the i^(th)−1        node defined as (α_(i−1)−α₀);    -   Δα_(i) ⁰ is the change in inclination angle at the i^(th) node        defined as (α_(i)−α₀);    -   (EI)_(i) is the product of Young's modulus and a moment of        inertia of the component at the i^(th) node; and    -   (EA)_(i) is the product of Young's modulus and a cross-sectional        area of the component at the i^(th) node.

For the first node, i=1 and the state vector V_(i) is expressed as,

V ₁ =T ₁ ×V ₀  (3).

Equation (3) expresses the state vector V₁ as a set of constrainedlinear equations for the well casing segment that can be solved todetermine the unknown forces present at node 1. For each subsequent nodei, the cross product of the node's transfer matrix and the referencenode's state vector is combined with prior cross products for nodes 1through i−1 to determine the state vector for node i, thus determiningthe unknown forces at each node i (i.e., F_(xi), F_(hi) and/or M_(i)).Once these forces are known, the axial force at a node can be computedas,

F _(ai) =F _(xi)×cos(α_(i))+F _(hi)×sin(α_(i))  (4).

In at least some illustrative embodiments, a transfer matrix method(TMM) is used to perform the combination of cross products. Using TMM,the combination of cross products producing the i^(th) node's statevector is expressed as,

V _(i)=(Π₁ ^(i) T _(i))×V ₀  (5).

Because each of the prior products of products for each node 1 throughi−1 have already been calculated, the product of products does not needto be recalculated for each node. Instead, each node's transfer matrixcan be combined with a cumulative transfer matrix, thus avoidingduplicative computations. For example, for a three node string thiswould be expressed as,

T _(acc) =T ₁ ; V ₁ =T _(acc) ×V ₀  (6),

T _(acc) =T _(acc) ×T ₂ ; V ₂ =T _(acc) ×V ₀=(T ₁ ×T ₂)×V ₀  (7), and

T _(acc) =T _(acc) ×T ₃ ; V ₃ =T _(acc) ×V ₀=(T ₁ ×T ₂ ×T ₃)×V ₀  (8).

The cross product T₁×T₂ has already been calculated in equation (7) andsaved as cumulative transfer matrix T_(acc), which is reused withoutrecalculation in equation (8).

It should be noted that the transfer matrix is not limited to thespecific embodiment of equation (2). For example, plugs such ascementing plugs present within the casing string and reductions in thecross-sectional area of the casing such as reduction 15 of FIG. 1 may berepresented by much simpler transfer matrices. In at least someillustrative embodiments, such plugs and reductions located at a node iare represented as,

$\begin{matrix}\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & F_{p}^{x} \\0 & 0 & 0 & 0 & 0 & 1 & F_{p}^{h} \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i} & (8)\end{matrix}$

where,

F_(p) ^(x) is a vertical force present on a plug or reduction located atthe node; and

E_(p) ^(h) is a horizontal force present on the plug or reduction.

Other transfer matrices may include, for example, parameters thatdescribe the load imposed on a casing string by a salt formation (i.e.,“salt loading”). A wide variety of transfer matrices suitable for usewith the methods described herein will become apparent to those ofordinary skill in the art, and all such variations of transfer matricesare within the scope of the present disclosure.

The algorithmic approach of equations (6) through (8) for computingequation (5) is suitable for implementation by software executing on acomputer system such as the illustrative system shown in FIG. 3. Bothhardware and software components of computer system 300 are shown, whichin at least some illustrative embodiments implement at least part of thematrix-based well casing string modeling shown as method 400 in FIG. 4(described in more detail below). Computer system 300 operates inaccordance with software (which may be stored on non-transitoryinformation storage media 340) and enables a user to interact with thesystem via keyboard 334, pointing device 335 (e.g., a mouse) and display336 to configure, control and monitor the execution of the matrix-basedwell casing string modeling.

Located within processing subsystem 330 of computer system 300 is adisplay interface 352, a processor 356, a peripheral interface 358, aninformation storage device 360, a network interface 362 and a memory370. Bus 364 couples each of these elements to each other and transportstheir communications. Network interface 362 enables communications withother systems (e.g., via the Internet with a central database serverhousing additional modeling parameters and suitable for saving theresults of the modeling). In accordance with user input received viaperipheral interface 358 and program instructions from memory 370 and/orinformation storage device 360, processor 356 processes input from theuser and applies it to the well casing string data to perform thedisclosed methods and present the results to the user. Storage device360 may be implemented using any number of known non-transitoryinformation storage media, including but not limited to magnetic disks,solid-state storage devices and optical storage disks.

Various software modules are shown loaded into memory 370 of FIG. 3,where they are each accessed by processor 356 for execution. Thesemodules include: user interface module, which processes user inputsprovided with keyboard 334 and pointing device 335 via peripheralinterface 358; vector definition module 374, which defines the statevector for each node; matrix definition module 376, which defines thetransfer matrix for a segment; cross product module 378, which computesthe cross product that updates the cumulative transfer matrix; transfermatrix method module 380, which uses the cumulative transfer matrix fromcross product module 378 to determine unknown state vector elements;parameter derivation module 382, which derives well componentmanufacturing parameters or well component centralizer positions; andpresentation module 384 which provides the derived manufacturingparameters or centralizer positions to manufacturing or operationspersonnel (e.g., by graphically presenting the dimensions of casingsegments or of centralizer positions along the length of the casingprior to cementing into place).

FIG. 4 shows an illustrative method that implements the above-describedmatrix-based modeling, at least part of which may be implemented bysoftware executing on computer system 300. It should be noted thatalthough the embodiment of FIG. 3 shows various software modulesexecuting on computer system 300, in other illustrative embodiments someor all of the modules may execute on two or more computers within anetworked and/or distributed system. Referring to both FIGS. 3 and 4,the state vector for the reference node (node 0) at the start of acasing string is defined (block 402; vector definition module 374),either via user input (user interface module 372) or using previouslystored data (e.g., data stored on information storage device 360). Nodeindex i is incremented from 0 to 1 and the total product is initializedto zero (block 402; TMM module 382). A state vector for the currenti^(th) node (here node 1) is defined in a manner similar to that usedfor the reference node (block 404; vector definition module 374), butwith at least one unknown state vector element.

If the segment associated with the current node is one that restrictsfluid flow, such as a plug or a casing cross-sectional area reduction(block 406; matrix definition module 376) the transfer matrix is definedin terms of one or more forces present at the restriction (block 408;matrix definition module 376). If the segment associated with thecurrent node is a well casing string, the transfer matrix is defined interms of the reference node's state vector, the previous node's statevector and/or the known elements of the current node's state vector(block 410; matrix definition module 376). Once the transfer matrix isdefined for node i, the cumulative transfer matrix T_(acc) is eitherinitialized as T₁ for i=1, or updated as the cross product of thecurrent node's transfer matrix T_(i) and T_(acc) for i>1 (block 412;cross product module 380). The cross product is then utilized todetermine the node's full state vector, which is used to determine theunknown element values of the current node's state vector (block 414;TMM module 380). In at least some illustrative embodiments, block 414 isskipped for the first node (i=1) if all the state vector values arealready known (e.g., if the values are readily measurable at a startingpoint at the surface).

If additional well casing string segments remain (block 418; TMM module380) node index i is incremented and the current node's state vectorbecomes the prior node's state vector (block 416; TMM module 380). Theabove-described process is then repeated for the next segment and nodealong the well casing string (blocks 404 through 418). If there are noadditional well casing string segments (block 418; TMM module 380), thepreviously unknown and now calculated elements of each state vector aresubsequently used as a basis for determining casing manufacturingparameters such as dimensions and composition, or as a basis forlocating centralizers to position the casing within a borehole (block420, parameter derivation module 382). The resulting manufacturingparameters or centralizer position are respectively provided ascomposition and/or dimensional specifications to manufacturingpersonnel, or as a position for a centralizer or stabilizer to welloperators/component installers (block 422, presentation module 384),ending the method (block 424).

In at least some illustrative embodiments, the calculated forces at eachnode along a casing string are indicated on a graphical representationof the well casing string. Once the forces have been determined, theaxial load (e.g., tension) present at a given node can be computed, forexample by using equation (4). Casing string parameters such as segmentlengths, wall thickness and material compositions may then be determinedfrom the computed axial load. These parameters provide the requiredcasing safety margins at a reduced cost when compared to existingmethods that overestimate the required casing string parameters. Inother illustrative embodiments, the positions of one or morecentralizers (determined based upon the computed and displayed forces)are on the casing string's graphical representation. The calculatedforces at each node are used to determine the side force to which acasing segment i (located between two nodes i and i+1) is subjected, forexample by using the equation,

SideForce_(i)=√{square root over (F _(x(i+1)) −F _(xi))²+(F _(h(i+1)) −F_(hi)))}{square root over (F _(x(i+1)) −F _(xi))²+(F _(h(i+1)) −F_(hi)))}  (9).

The contact points between the casing and borehole wall can bedetermined from the state vector V_(i) and the well trajectory. Thecomputed side force and the contact points are then used to determine asuitable centralizer(s) and the best centralizer position(s), forexample, at the contact point(s) between the casing segment and theborehole wall.

Numerous other modifications, equivalents, and alternatives, will becomeapparent to those skilled in the art once the above disclosure is fullyappreciated. For example, although the embodiments described use the TMMto determine the transfer matrices, other analytical methods are alsosuitable to determine transfer matrices used to determine the unknownelements of a node of interest. Further, although the examples providedare applied within the context of static modeling, static snapshotsrepeatedly performed over time may be combined to provide dynamic aswell as near-real-time or real-time modeling of the well casing string(e.g., to predict the loading on a well casing string as a cementingplug progresses down the string). Additionally, although the disclosedembodiments describe modeling well casing strings, any of a wide varietyof well components may be modeled to determine the manufacturing and/oroperating parameters of said components. These well components includebut are not limited to drillstrings, workstrings, production strings andcoiled tubing stings. Other well components that restrict fluid flowwithin a running tubular string (e.g., packers) are also within thescope of the disclosure. It is intended that the following claims beinterpreted to embrace all such modifications, equivalents, andalternatives where applicable.

What is claimed is:
 1. A method for determining manufacturing oroperating parameters for a deviated downhole well component, the methodcomprising: representing a tubular string as a sequence of nodesseparated by segments, said nodes being numerable from i=1 to N with aninitial, mechanically constrained reference node representable with i=0,and each node being associated with a state vector describing a positionof the corresponding node and one or more forces present at saidcorresponding node; determining a sequence of transfer matrices enablingthe determination of an i^(th) node's state vector from an i^(th)−1node's state vector; defining values of an initial state vector for thereference node; applying the transfer matrices to obtain values for eachof the state vectors; deriving from at least one of the state vectors aparameter value for said component, the parameter value being in a setconsisting of a composition, manufacturing dimensions, and a positionfor a centralizer or stabilizer; and specifying a component having saidparameter value.
 2. The method of claim 1, wherein said specifyingincludes providing the composition or a dimensional specification to amanufacturer of said component.
 3. The method of claim 1, wherein saidspecifying includes providing the position for the centralizer orstabilizer to an installer of said component.
 4. The method of claim 1,wherein each state vector comprises a vertical position u_(i), ahorizontal position v_(i), and an inclination angle α_(i), associatedwith node i; and further comprises a vertical force F_(xi), a horizontalforce F_(hi) and a bending moment M_(i) present at node i; and whereinthe state vector is representable as [u_(i), v_(i), α_(i), F_(xi),F_(hi), M_(i), 1]^(T).
 5. The method of claim 4, wherein the transfermatrix for the i^(th) node, said i^(th) node associated with a tubularsegment, is representable as: $\begin{bmatrix}1 & 0 & {- l_{i}^{h}} & \left( {\frac{\left( l^{h_{i}} \right)^{B}}{6 \times ({EI})_{i}} + \frac{l_{i}^{x}}{({EA})_{i}}} \right) & 0 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{h}}} \\0 & 1 & l_{i}^{x} & 0 & \left( {{- \frac{\left( l_{i}^{x} \right)^{B}}{6 \times ({EI})_{i}}} + \frac{l_{i}^{h}}{({EA})_{i}}} \right) & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{x}}} \\0 & 0 & 1 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & \frac{\sqrt{\left( l_{i}^{x} \right)^{2} + \left( l_{i}^{h} \right)^{2}}}{({EI})_{i}} & {\Delta \; \alpha_{i}^{0}} \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & l_{i}^{h} & {- l_{i}^{x}} & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i}$ where, l_(i) ^(h) is a horizontal distance defined as(v_(i)−v_(i−1)); l_(i) ^(x) is a vertical distance defined as(u_(i)−u_(i−1)); Δα_(i−1) ⁰ is a change in inclination angle at thei^(th)−1 node defined as (α_(i−1)−α₀); Δα_(i) ⁰ is a change ininclination angle at the i^(th) node defined as (α_(i)−α₀); (EI)_(i) isa product of Young's modulus and a moment of inertia of the component atthe i^(th) node; and (EA)_(i) is a product of Young's modulus and across-sectional area of the component at the i^(th) node.
 6. The methodof claim 4, wherein said deriving includes deriving an axial forceF_(ai) present at the i^(th) node.
 7. The method of claim 4, wherein thetransfer matrix for the i^(th) node, said i^(th) node associated with aflow restriction, is representable as: $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & F_{p}^{x} \\0 & 0 & 0 & 0 & 0 & 1 & F_{p}^{h} \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i}$ where, F_(p) ^(x) is a vertical force present on aplug located at the i^(th) node; and F_(p) ^(h) is a horizontal forcepresent on the plug.
 8. The method of claim 1, wherein the N^(th) nodeis also mechanically constraint.
 9. The method of claim 1, wherein thecomponent comprises a running string selected from the group consistingof a well casing string, a drillstring, a production string and a coiltubing.
 10. The method of claim 9, wherein the running string comprisesa tapered segment, a cross-section size change, a packer or a plug. 11.A system that determines manufacturing and operating parameters for adeviated downhole well component, the system comprising: a memory havingdeviated downhole well component modeling software; and one or moreprocessors coupled to the memory, the software causing the one or moreprocessors to: represent a tubular string as a sequence of nodesseparated by segments, said nodes being numerable from i=1 to N with aninitial, mechanically constrained reference node representable with i=0,and each node being associated with a state vector describing a positionof the corresponding node and one or more forces present at saidcorresponding node; determine a sequence of transfer matrices enablingthe determination of an i^(th) node's state vector from an i^(th)-1node's state vector; define values of an initial state vector for thereference node; apply the transfer matrices to obtain values for each ofthe state vectors; derive from at least one of the state vectors aparameter value for said component, the parameter value being in a setconsisting of a composition, manufacturing dimensions, and a positionfor a centralizer or stabilizer; and specify a component having saidparameter value.
 12. The system of claim 11, wherein the one or moreprocessors specify said component at least in part by providing thecomposition or a dimensional specification to a manufacturer of saidcomponent.
 13. The system of claim 11, wherein the one or moreprocessors specify said component at least in part by providing theposition for the centralizer or stabilizer to an installer of saidcomponent.
 14. The system of claim 11, wherein each state vectorcomprises a vertical position u_(i), a horizontal position v_(i), and aninclination angle α_(i), associated with node i; and further comprises avertical force F_(xi), a horizontal force F_(hi) and a bending momentM_(i) present at node i; and wherein the state vector is representableas [u_(i), v_(i), α_(i), F_(xi), F_(hi), M_(i), 1]^(T).
 15. The systemof claim 12, wherein the transfer matrix for the i^(th) node, saidi^(th) node associated with a tubular segment, is representable as:$\begin{bmatrix}1 & 0 & {- l_{i}^{h}} & \left( {\frac{\left( l^{h_{i}} \right)^{B}}{6 \times ({EI})_{i}} + \frac{l_{i}^{x}}{({EA})_{i}}} \right) & 0 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{h}}} \\0 & 1 & l_{i}^{x} & 0 & \left( {{- \frac{\left( l_{i}^{x} \right)^{B}}{6 \times ({EI})_{i}}} + \frac{l_{i}^{h}}{({EA})_{i}}} \right) & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & {l_{i}^{x} + {\Delta \; \alpha_{i - 1}^{0} \times l_{i}^{x}}} \\0 & 0 & 1 & {- \frac{\left( l_{i}^{h} \right)^{2}}{2 \times ({EI})_{i}}} & \frac{\left( l_{i}^{x} \right)^{2}}{2 \times ({EI})_{i}} & \frac{\sqrt{\left( l_{i}^{x} \right)^{2} + \left( l_{i}^{h} \right)^{2}}}{({EI})_{i}} & {\Delta \; \alpha_{i}^{0}} \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & l_{i}^{h} & {- l_{i}^{x}} & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i}$ where, l_(i) ^(h) is the horizontal distance definedas (v_(i)−v_(i−1)); l_(i) ^(x) is the vertical distance defined as(u_(i)−u_(i−1)); Δα_(i−1) ⁰ is the change in inclination angle at thei^(th)−1 node defined as (α_(i−1)−α₀); Δα_(i) ⁰ is the change ininclination angle at the i^(th) node defined as (α_(i)−α₀); (EI)_(i) isthe product of Young's modulus and a moment of inertia of the componentat the i^(th) node; and (EA)_(i) is the product of Young's modulus and across-sectional area of the component at the i^(th) node.
 16. The systemof claim 14, wherein the one or more processors derive said parametervalue at least in part by deriving an axial force F_(αi), present at thei^(th) node.
 17. The system of claim 14, wherein the transfer matrix forthe i^(th) node, said i^(th) node associated with a flow restriction, isrepresentable as: $\begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & F_{p}^{x} \\0 & 0 & 0 & 0 & 0 & 1 & F_{p}^{h} \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}_{i}$ where, F_(p) ^(x) is a vertical force present on aplug located at the i^(th) node; and F_(p) ^(h) is a horizontal forcepresent on the plug.
 18. The system of claim 11, wherein the N^(th) nodeis also mechanically constraint.
 19. The system of claim 11, wherein thecomponent comprises a running string selected from the group consistingof a well casing string, a drillstring, a production string and a coiltubing.
 20. The system of claim 19, wherein the running string comprisesa tapered segment, a cross-section size change, a packer or a plug.